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Some applications of $$K$$-theory to framed bordism: E-invariant and transfer. (English) Zbl 0982.55500
Bonn: Univ. Bonn, Mathematisch-Naturwissenschaftliche Fakultät (Habil.), 115 p. (1979).
From the introduction: We study $$\pi^S_*(P_\infty\mathbb{C})$$ using as the main tools the $$e$$-invariant of Adams and various transfer maps. The $$e$$-invariant describes the information about $$\pi^S_*(X)$$ obtainable using $$K$$-theory and the transfer maps relate $$\pi^S_*(P_\infty\mathbb{C})$$ to the stable homotopy of spheres and allow us to construct elements in $$\pi^S_*(P_\infty\mathbb{C})$$.

##### MSC:
 55Q10 Stable homotopy groups 55Q52 Homotopy groups of special spaces
##### Keywords:
transfer map; complex projective space